-A machine P can print one-lakh books in 8 hours; machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 A.M. while machine P is closed at 11 A.M. and the remaining two machines complete work. Approximately, at what time will the work (to print one-lakh books) be finished?
Question
-A machine P can print one-lakh books in 8 hours; machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 A.M. while machine P is closed at 11 A.M. and the remaining two machines complete work. Approximately, at what time will the work (to print one-lakh books) be finished?
Solution
Sure, let's break it down:
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Machine P can print one-lakh books in 8 hours. This means it prints at a rate of 1 lakh/8 hours = 12,500 books per hour.
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Machine P starts at 9 A.M. and stops at 11 A.M., so it works for 2 hours. In this time, it prints 2 hours * 12,500 books/hour = 25,000 books.
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This leaves 1 lakh - 25,000 = 75,000 books to be printed by machines Q and R.
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Machine Q can print one-lakh books in 10 hours, so it prints at a rate of 1 lakh/10 hours = 10,000 books per hour.
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Machine R can print one-lakh books in 12 hours, so it prints at a rate of 1 lakh/12 hours = 8,333 books per hour.
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Together, machines Q and R print at a rate of 10,000 books/hour + 8,333 books/hour = 18,333 books per hour.
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To print the remaining 75,000 books, machines Q and R will take 75,000 books / 18,333 books/hour = approximately 4.09 hours.
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Since machine P stopped at 11 A.M., and machines Q and R take approximately 4.09 hours to finish the remaining work, the work will be finished at about 11 A.M. + 4.09 hours = approximately 3:05 P.M.
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